Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Abouhawwash, Mohamed; Seada, Haitham; Deb, Kalyanmoy

doi:10.1016/j.cor.2016.04.026

Cited by 24 publications

(11 citation statements)

References 29 publications

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“…We also need to explore more ways of bridging the gap between this field and elements from Operations Research, such as mathematical programming [154]. Another one is the use of the Karush-Kuhn-Tucker optimality conditions to estimate proximity of a solution to the Pareto optimal set [155]. All in all, diversity, heterogeneity and synergy between different disciplines must be ensured within the community working in order to attain more disruptive and scientifically valuable advances not only in multi-/many-objective optimization, but also in other areas within bio-inspired optimization.…”

Section: Multi-and Many-objective Optimizationmentioning

confidence: 99%

Bio-inspired computation: Where we stand and what's next

Ser

Osaba

Molina

et al. 2019

Swarm and Evolutionary Computation

481

106

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Section: Multi-and Many-objective Optimizationmentioning

confidence: 99%

Bio-inspired computation: Where we stand and what's next

Ser

Osaba

Molina

et al. 2019

Swarm and Evolutionary Computation

481

106

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“…(5) Non-dominated solutions that have poorly convergence can be identified using KKTPM value and then improves it by using an ASF based local search operator [1].…”

Section: M Andmentioning

confidence: 99%

KKT Proximity Measure Versus Augmented Achievement Scalarization Function

Abouhawwash¹,

Jameel²

2018

IJCA

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KKT proximity measure (KKTPM) is use as metric for obtained how we are close to the from a corresponding Pareto-optimal (PO) point without any knowledge about the true optimum point. This metric use one such common a scalarization method that also guarantees to find any PO solution that is achievement scalarizing function (ASF) method. Since that KKTPM formulation is based on augmented achievement scalarizing function (AASF) to avoid weak PO solutions. This paper studies a relation between KKTPM values and AASF values. Aim of this study to know the advantage and disadvantage of both measures. Also, this paper discusses some special cases to know the merits of both measures and to confirm that KKT proximity measure is an essential measure for convergence. In addition, this study investigates the correlation plot between these two measures for ZDT test problems, results show the difference in values and therefore cannot obtain a perfect correlation between KKTPM values and AASF values. Hence, it can be said that KKT proximity measure is better.

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“…The authors propose to use a proximity measure which is based on this relaxation and hence, based on the KKT error. A possibility to use this approach also for multi-objective optimization is to first scalarize the vector-valued optimization problem to a single-objective optimization problem, which was discussed in [7], [2], and [1]. Within this paper, we avoid the detour of a scalarization.…”

Section: Introductionmentioning

confidence: 99%

Proximity measures based on KKT points for constrained multi-objective optimization

Eichfelder

Warnow

2020

J Glob Optim

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An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.

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Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Cited by 24 publications

References 29 publications

Bio-inspired computation: Where we stand and what's next

Bio-inspired computation: Where we stand and what's next

KKT Proximity Measure Versus Augmented Achievement Scalarization Function

Proximity measures based on KKT points for constrained multi-objective optimization

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